For the FL approach, we use a slightly modified version of Federated Averaging (FedAvg) [1]}:
(i) First, all local models of the \(K\)  hospitals are initialized with the same set of starting weights \(\theta ^0\) .
(ii) By performing local training for \(E\)  local epochs, each of the participating hospitals derives an updated set of weight parameters \(\theta _k\) . The fraction of participating hospitals per round is \(C\) . The local objective is similar to Equation REF .
(iii) After local training, a global model \(f^{FL}(\cdot ,\theta )\)  is created by averaging all \(\theta _k\)  to one set of parameters \(\theta \) .
(iv) These averaged weights are then sent back to the hospitals, which overwrite their local weights with the new ones.
(v) Afterwards, an ES score \(s\)  is calculated by evaluating the local models on the respective validation set of each client \(k\)  and then averaging the results: \(s=\sum ^{K}_{k=1} \frac{n_k}{n} M(\bf {\hat{y}}_k,\bf {y}_k)\) . The above is repeated from step (ii) until the validation scores suggest an optimal set of weights \(\theta ^{FL}\)  and ES is activated. Here, the objective is to optimize the global model \(f^{FL}(\cdot ,\theta )\)  by calculating:
